Grades
Standard
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and [...]
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using [...]
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division [...]
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the [...]
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic [...]
Interpret parts of an expression, such as terms, factors, and coefficients.*
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as [...]
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 [...]
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the [...]
Factor a quadratic expression to reveal the zeros of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Use the properties of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 [...]
(+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that [...]
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use [...]
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role [...]
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, [...]
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another [...]
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x [...]
(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant [...]
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the [...]
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are [...]
(+) Add, subtract, and multiply matrices of appropriate dimensions.
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies [...]
Interpret expressions that represent a quantity in terms of its context.*
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
(+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors [...]
Define appropriate quantities for the purpose of descriptive modeling.*
(+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*
(+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with [...]
Know there is a complex number i such that i^2 = −1, and every complex number has the form a [...]
(+) Perform operations on vectors. Multiply a vector by a scalar.
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v(sub [...]
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain [...]
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation [...]
(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of [...]
Solve quadratic equations with real coefficients that have complex solutions.
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate [...]
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a [...]
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of [...]
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting [...]
Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an [...]
Grades
Standard
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and [...]
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using [...]
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division [...]
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the [...]
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic [...]
Interpret parts of an expression, such as terms, factors, and coefficients.*
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as [...]
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 [...]
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the [...]
Factor a quadratic expression to reveal the zeros of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Use the properties of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 [...]
(+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that [...]
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use [...]
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role [...]
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, [...]
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another [...]
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x [...]
(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant [...]
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the [...]
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are [...]
(+) Add, subtract, and multiply matrices of appropriate dimensions.
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies [...]
Interpret expressions that represent a quantity in terms of its context.*
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
(+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors [...]
Define appropriate quantities for the purpose of descriptive modeling.*
(+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*
(+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with [...]
Know there is a complex number i such that i^2 = −1, and every complex number has the form a [...]
(+) Perform operations on vectors. Multiply a vector by a scalar.
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v(sub [...]
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain [...]
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation [...]
(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of [...]
Solve quadratic equations with real coefficients that have complex solutions.
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate [...]
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a [...]
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of [...]
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting [...]
Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an [...]